Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 https://doi.org/10.1186/s41445-018-0014-7 The Journl of Glol Positioning Systems ORIGINAL ARTICLE Dynmic chrcteristic of the forth rod ridge estimted with GeoSHM Xiolin Meng 1*, Ruijie Xi 1,2 nd Yilin Xie 1 Open Access Astrct The importnce of ridge helth monitoring nd mngement hs een recognized y uthorities of long-spn ridges throughout the world in recent yers. The GeoSHM consortium, led y the University of Nottinghm, ws wrded Fesiility Study (FS) grnt in 2013 y the Europen Spce Agency (ESA) to investigte how to use integrted GNSS nd Erth Oservtion technologies for the structurl helth monitoring of lrge ridges. During the GeoSHM FS period smll monitoring system ws instlled on the Forth Rod Bridge in Scotlnd nd the consortium hve gthered huge dt sets nd rich experience regrding the design nd implementtion of GeoSHM ccording to essentil user needs. This pper, sed on the dt from GNSS receivers instlled on the two middle spn sites nd top of the southern tower of the Forth Rod Bridge, intends to revel the dynmic chrcteristics of the ridge. By using moving verge filter, Fst Fourier Trnsformtion (FFT) nd the pek-picking pproch, the threedimensionl (3D) displcement time series under mient excittion were decomposed into long-period movement nd dynmic virtion response. The results demonstrte tht the movement of the Forth Rod Bridge in lterl direction is minly cused y wind loding, nd the correltion is out 0.7. In verticl direction, the displcements of middle spn sites under the norml trffic lodings cn rech 0.3 m nd ecuse of the min cle linking the middle spn nd top of the tower, the longitudinl movement of the southern tower top site hs high correltion with the verticl displcements of middle spn sites. It hs een found tht due to the stiffness of the tower the trend terms inside lterl nd verticl time series minly consist of multipth effect nd qusi-sttic displcement. The dynmic virtion frequencies nd corresponding motion mplitudes were lso extrcted. It is found tht the first nturl frequencies of the middle spn of the Forth Rod Bridge re 0.065 Hz, 0.15 Hz nd 0.104 Hz for lterl, longitudinl nd verticl directions, respectively. For the south tower, virtion frequencies of 0.18 Hz cn e seen in ll three directions, ut 0.104 Hz is only visile in longitudinl component ecuse of the cles linking the tower nd middle spn. It demonstrtes tht with proper dt mining pproch oth the low frequency responses nd dynmic virtion chrcteristics of lrge ridge under mient lodings cn e extrcted from GNSS dt sets. Thus, GeoSHM cn e used y ridge owners s n effective tool to ssess the opertionl conditions of the ridge. Keywords: GeoSHM, Displcement monitoring, The forth rod ridge, Pek-picking pproch, Dynmic chrcteristics, Amient excittion * Correspondence: xiolin.meng@nottinghm.c.uk 1 Nottinghm Geosptil Institute, The University of Nottinghm, Nottinghm NG7 2TU, UK Full list of uthor informtion is ville t the end of the rticle The Author(s). 2018 Open Access This rticle is distriuted under the terms of the Cretive Commons Attriution 4.0 Interntionl License (http://cretivecommons.org/licenses/y/4.0/), which permits unrestricted use, distriution, nd reproduction in ny medium, provided you give pproprite credit to the originl uthor(s) nd the source, provide link to the Cretive Commons license, nd indicte if chnges were mde.
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 2 of 15 Fig. 1 The Forth Rod Bridge in the UK Introduction Glol Nvigtion Stellite Systems (GNSS), especilly Glol Positioning System (GPS) technology hs een employed to monitor lrge ridge deformtion for more thn 20 yers (Meng 2002). Compred with trditionl techniques, GNSS cn provide continuous, utomted, ll-wether nd highly ccurte mesurements while it is difficult for other sensors such s n ccelerometer to detect oth the sttic nd dynmic deformtions of the structure (Meng et l. 2004; Meng et l. 2006; Li et l. 2006; Yi et l. 2013; Yu et l. 2016). GNSS techniques cn e used effectively to monitor long suspension/ cle-styed nd medium ridges (Xu et l. 2002; Wtson et l. 2007; Roerts et l., 2012; Yu et l. 2014). Fig. 2 The overll GeoSHM system rchitecture
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 3 of 15 Fig. 3 The GNSS receiver distriution nd the defined ridge coordinte system Mny technicl issues hve lso een ddressed, such s the impct of GPS stellite nd pseudolite geometry on structure deformtion monitoring (Meng et l. 2004), dynmic multipth in structurl helth monitoring of ridges (Moschs nd Stiros, 2014), ridge monitoring with high frequency GPS (Roerts et l., 2004), nd using RTK-GPS to mesure wind-induced response (Tmur et l. 2002), etc. However, there re ovious disdvntges of using GNSS to monitor ridge deformtion. For exmple, the low smpling rte nd high level of oservtion noise mke it impossile to detect reltively high virtion ridge frequencies (Meng 2002; Meng et l. 2007; Breuer et l. 2015; Górski, 2017). Thus, mny reserches hve mde to use n integrted monitoring system with dul frequency GNSS receivers nd ccelerometers to detect the dynmics informtion which cn significntly improve the overll system performnce (Roerts et l., 2001; Yu et l. 2014; Meng et l. 2014). Meng et l. (2014) presented n optiml GPS/ccelerometer integrtion lgorithm for monitoring the verticl structurl dynmics. Moschs nd Stiros (2011) lso chieved the dynmic displcements nd modl frequencies of short-spn pedestrin ridge using GPS nd n/the ccelerometer. Xiong et l. (2017) proposednafec mixed filtering lgorithm to eliminte the multipth errors nd rndom noise from GNSS nd ccelerometer dt. GNSS receivers nd ccelerometers, nevertheless, cn only determine the ridge responding informtion. Enough dt on loding nd responding should lso e collected if we wnt to correctly ssess the helth of ridge (Sumitoro et l., 2011; Erdoğn nd Güll, 2009; Meng et l. 2016). Thus, n integrl mngement system with different sensors to mesure (minly GNSS, interferometric SAR, ccelerometer) nd quntify the induced excittion (wind, trffic nd even erthqukes etc.) nd its corresponding response, is importnt nd needs to e crefully designed. The GeoSHM (GNSS nd Erth Oservtion for Structurl Helth Monitoring of Bridges) project supported y the Europen Spce Agency is system tht uses integrted GNSS nd Erth Oservtion technologies for structurl helth monitoring of lrge ridges nd in its fesiility study the consortium used the Forth Rod Bridge in Scotlnd s its tested ridge. In the FS stge from August 2013 to Mrch 2015, we instlled smll footprint sensor system on the ridge (Meng et l. 2016). In the demonstrtion Fig. 4 GeoSHM ntenn setting-ups t monitoring sttions
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 4 of 15 Tle 1 The detils of the monitoring sttions Sttion Nme Loction Bseline Length (m) Smpling (Hz) Receivers (ntenn) SHM2 Middle Spn 1528.09 20 Leic Geosystem GR10 (LEIAR10) SHM3 Middle Spn 1527.97 20 Leic Geosystem GR10 (LEIAR10) SHM4 South Tower 1032.67 20 Leic Geosystem GR10 (LEIAR10) stge from Mrch 2016 to Mch 2018, we re focusing on ddressing the mjor drwcks of the GeoSHM FS Project nd developing smrt dt strtegy to fully reflect the end user needs. In this pper, we will use the GNSS receivers instlled on the middle spn nd top of the tower of the Forth Rod Bridge in the GeoSHM project to investigte the dynmic chrcteristics of the ridge. Bsed on FFT nd the pek-picking pproch, the displcements time series under mient excittion were decomposed into longperiod movement nd dynmic virtion response, nd the mechnism of the movement nd the nturl frequencies were lso nlysed. Forth rod ridge nd GeoSHM The Forth Rod Bridge crosses the Firth of Forth nd links the north of Scotlnd with Edinurgh nd the south of the A90 rod. The ridge length is 2.5 km nd the min spn length is 1006 m. It opened in 1964 nd the trffic volume hs lredy surpssed 24 million vehicles per nnum, round 11 times of the trffic volume in 1965. Fig 1 is the picture of the Forth Rod Bridge. The min im of the GeoSHM is to use different kinds of sensors to mesure (minly GNSS, interferometric SAR, ccelerometer) nd quntify the induced excittion (wind, trffic nd even erthqukes etc.) nd its corresponding response, nd mke comprisons with theoreticlly designed thresholds or models of the structure for the evlution of the helth condition of ridges (Meng et l. 2016). Figure 2 shows the overll structure of GeoSHM tht consists of sensor network, dt trnsmission module nd su-systems for dt processing nd visulistion. The sensor system consists of: one reference GNSS sttion set on the top of the office uilding of the Forth Rod Bridge, three monitoring GNSS sttions with two sets on ech side of the middle spn nd one set on the west side of southern tower, nd two ultrsonic nemometers with one on the west side of middle spn nd the other close to southern tower site. Figure 3 shows the distriution of the sensors nd Fig. 4 gives the GNSS ntenns nd the nemometers locted t the middle spn nd top of the tower. More detils out monitoring Fig. 5 Displcement time series of Middle spn
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 5 of 15 Fig. 6 Displcement time series of top of the tower Fig. 7 FFT result of SHM2
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 6 of 15 Fig. 8 FFT result of SHM3 Fig. 9 FFT result of SHM4
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 7 of 15 Tle 2 Dominnt frequencies detected from displcement time series. (Hz) Sttion Nme Lterl (Y B ) Longitudinl (X B ) Height (Z B ) SHM2 0.065 0.268 0.342 1.702 0.15 0.104 0.205 0.268 SHM3 0.065 0.268 0.342 1.702 0.15 0.104 0.205 0.268 SHM4 0.18 0.104 0.15 0.18 0.18 sttions cn e seen in Tle 1. Automted dt cquisition is crried out y these sensors nd the cquired rel-time dt re sent, vi the optic fire network lid underneth the ridge, to locl hu efore they re stremed to the dt processing centre set up t the University of Nottinghm vi pulic Internet. The received rw dt sets re processed in rel time or post-processing mnner. Methods GPS dt processing As previously mentioned, the GNSS dt collected cn e processed in rel-time nd post-processing mnner modes. In this pper, Rel-Time Kinemtic (RTK) mode ws pplied to otin displcement time series of monitoring sttions (Elnwy et l. 2013). Since the short selines re used (Tle 1) in GNSS dt processing, the stellite-dependent terms, such s stellite clock offsets, nd crrier phse frctionl ises, the distnce-dependent terms, such s tropospheric nd ionospheric dely, nd stellite orit errors could e neglected in doule-difference (Breuer et l. 2015; Górski, 2017). Thus, there re only coordinte prmeters nd doule-difference miguity prmeters left in the prmeter list to e estimted. For the purpose of fst miguity fixing, dul-frequency phse oservtions re used. The unknown prmeters re estimted y Klmn filter, nd the coordinte prmeters with flot miguities cn e otined. Then the LAMBDA method will e pplied to otin the miguity fixed resolutions. During the dt processing, the rodcst ephemeris ws used to clculte the orit of stellites. The elevtion cutoff ngle ws set to 10, nd the elevtion relted stochstic model ws used for weighting the rndom oservtion errors. The outputs of the GNSS softwre were instntneous Crtesin coordintes of monitoring sttions in the WGS84 coordinte system (X, Y, Z) nd the seline components (N, E, U) formed from ech monitoring sttion to the reference sttion SHM1. However, locl Bridge Coordinte System (BCS) (X B, Y B, Z B ) should e defined for nlysis purpose (Meng et l. 2016). X B xis ws formed y SHM2 nd SHM4 nd points to the longitudinl direction of the ridge s shown in Fig. 3. Fig. 10 Long-period movement component for middle spn nd () wind speed time series in lterl (Y B ) component. The correltion coefficients etween displcement nd wind speed time series re shown in the figure ()
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 8 of 15 c d e Fig. 11 Dynmic virtion response of middle spn nd corresponding dominnt frequency signl extrcted in lterl (Y B ) component Then, Y B nd Z B re correspond to the lterl nd height directions. Coordintes in BCS cn e otined y trnsforming from WGS84 with 2D similrity trnsformtion (Eq. (1)). The zimuth of the ridge is defined α. 0 1 0 X B @ Y B A ¼ @ Z B 10 cos sin 0 sin cos 0 A@ 0 0 1 N E U 1 A ð1þ In terms of displcement time series, the men vlues cn e removed y Eq. (2) to limit the displcements in ll components round zero. 0 1 0 1 0 1 dx Bi X Bi @ dy Bi A ¼ @ Y Bi A 1 X @ n dz Bi Z Bi X Bi Y Bi Z Bi A ð2þ where (dx Bi, dy Bi, dz Bi ) re the displcements over every recording intervl, n represents the totl numer of the oservtion epochs, nd (i = 1, 2,, n). Frequency domin decomposition with pek-picking pproch In generl, displcement time series in the ith direction δ i (t) of structure in time t cn e expressed s follows (Hristopulos et l. 2007; Erdoğn nd Güll, 2009): δ i ðþ¼m t i ðþþd t i ðþþn t i ðþ; t t ft 1 ; t 2 ; ; t N g ð3þ where m i (t) is the long-period component or low frequency response of the time series, d i (t) is the dynmic virtion component, nd n i (t) is rndom noise from vrious sources. Then, filtering procedure is pplied to the series so s to prtilly eliminte the effect of noise in the series nd to nlyse the mechnism of the low frequency trend nd demonstrte the periodic components. In this pper, simple moving verge filter with step of pproximtely 4 s (Moschs nd Stiros 2011)
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 9 of 15 Fig. 12 Long-term movement component for middle spn in height (Z B ) component nd for top of the tower in longitudinl (X B ) component ws employed to seprte the long-period component of the time series m i (t). After the long-period component nlysis, the dynmic virtion response d i (t) should e extrcted y proper digitl filter. In this pper, pek-picking pproch for extrcting structurl virtion frequencies nd corresponding mplitudes proposed y Meng et l. (2007) ws used. This pproch consists of FFT lgorithm for precisely detecting locl dominnt frequencies nd Cheyshev type I digitl ndpss filter for identifying specific frequencies nd the corresponding virtion mplitude of the frequencies (Meng et l. 2007). Results This section demonstrtes the long-period response of the ridge nd the detection frequencies from mient virtion, nd corresponding mplitude, using the ove-mentioned pek-picking pproch. Monitoring results nd preliminry nlysis In this pper, the dt from July 25th 2017 were selected to do the displcement nlysis. By tking the high smpling rte of GNSS dt into considertion, the results from 16:00 to 17:00 re shown in the following. Figures 5 nd 6 plot the time series of the sttion displcements t the middle spn nd top of the tower. As it is shown, virtions hppened oviously in ll three directions. The chngele rnges in the longitudinl (X B ) nd height (Z B ) direction were within 5 cm nd 30 cm, respectively. The displcements in the lterl (Y B ) direction were smller in the mplitude of out 8 cm. However, rising trend cn e oviously seen. It my e result of the wind loding. As for SHM4, t the top of the tower, only the longitudinl (X B ) direction shows high mplitude displcement with out 6 cm. In the lterl (Y B ) nd height (Z B ) directions, the qusi-sttic displcements nd high frequency noise cn e oserved. It lso should e noticed tht the mplitude etween 16:30 nd 16:40 ecomes higher. The displcements shown in Figs 5 nd 6 were nlysed y the FFT (Figs 7, 8 nd 9). From Figs. 7, 8 nd 9, the locl dominnt frequencies cn e identified nd extrcted, which re listed in Tle 2. From the tle, we cn see tht SHM2 nd SHM3 shred the sme dominnt frequencies in ll directions. Tht is ecuse they re just locted t oth sides of the middle spn. SHM4 hd one dominnt frequency (0.18 Hz), in three directions, different from those of middle spn, which is the nturl frequency for the tower. The other two frequencies cn lso e found in the middle spn, which will e explined in section 4.2. Low frequency response nd dynmic virtion nlysis In this section, the displcement time series were decomposed into low frequency response (Long-period component: including qusi-sttic displcement nd ckground noise) nd dynmic virtion signl (Short-period component: contins the dynmic displcement of the oscilltion signl plus multipth noise). The long-period component
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 10 of 15 c d Fig. 13 Dynmic virtion response of middle spn nd corresponding dominnt frequency signl in height (Z B ) component ws otined y moving verge filter nd the dynmic virtion responses were extrcted y the eight-order Type 1 Cheyshev ndpss digitl filters with pss-nd nd stop-nd frequencies. The pss-nd ripple is 1 db. Figure 10 shows the long-period component of the displcement t middle spn in lterl (Y B ) direction. It cn e seen tht the time series of two monitoring sites mtch well with ech other. Tht mens the middle spn moves s whole ody under the lods. Figure 10 gives the wind speed in the sme session. To etter understnd the reltionship etween displcements nd wind lodings, the correltion coefficient etween them ws clculted y Eq. (4) X n ðx i xþðy i yþ i¼1 Rx; ð yþ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X n ðx i xþ 2 Xn ðy i yþ 2 i¼1 i¼1 ð4þ where n is the length of the time series,(i = 1,2,,n), nd x; y re the men vlue of time series x,y. We cn see tht the correltion coefficient etween the two displcement time series nd wind series re 0.72 nd 0.714, which mens the movements of the middle spn hve high correltion with the wind. During this hour, the wind direction ws ginst the Y coordinte xis, so they hve negtive correltion. According to the nlysis ove, we know tht, in lterl (Y B ) component, the movement of the middle spn is minly cused y the wind lods, which ccords with other reserchers results (Wng et l., 2016). According to Meng et l. (2007), the structurl mode prmeters such s nturl frequencies nd mode shpes cn e extrcted from responding mesurements under mient excittion lodings due to their convenience nd cost-effectiveness. Figure 11 shows typicl exmple of extrcted nturl frequencies nd corresponding mplitudes from displcement in lterl (Y B ) direction of
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 11 of 15 c Fig. 14 Long-term () nd virtion signls () decomposed from longitudinl (XB) component of middle spn, nd the dominnt frequency signl (c) extrcted from displcement c Fig. 15 Dynmic virtion signls for top of the tower
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 12 of 15 c d Fig. 16 The dominnt frequency signls extrcted from displcement of top of the towers. The cutoff elevtion is 10 in GPS dt processing the middle spn. As Górski (2017) mentioned, the frequency of GNSS time series under 0.05 Hz is minly trend signl nd low frequency ckground noise. From previous FFT nlysis, the dominnt frequencies re ll over 0.05 Hz nd limited to 1.1 Hz. In this cse, the time series in lterl (Y B ) direction of the middle spn were filtered using the eight-order Type 1 Cheyshev high-pss digitl filter with pss-nd 0.05 Hz nd stop-nd 1.1 Hz, which is shown in Fig. 11-e, show the locl frequencies series extrcted using very nrrow pss nd filter round the dominnt frequencies in Tle 2. The figure only gives the series when there is the mximum mplitude. As it is shown, the mplitude of first nturl frequency under mient lods is significntly lrger thn other frequencies. The mplitude of second nd third nturl frequencies due to wind is t out 1 mm level nd the forth is less thn 1 mm. Tht mens the first nturl frequency is the solute dominnt frequency in the dynmic virtion signl nd it should e pid more ttention in the SHM. In the height (Z B ) component of the middle spn, trffic lods re the min fctors responsile for the displcements (Wng et l., 2016).Atthemiddlespn, the displcement in the height direction cn rech to 30 cm. Figure 12 gives the long-period component of the displcement time series. The sme s lterl (Y B ) direction,thetimeseriesforthetwosttionsgreewith ech other. Becuse the min cle links the middle spn nd top of the tower, the displcements in longitudinl (X B ) direction of the tower re shown in Fig. 12. Bsed on Eq. (4), the correltion coefficients etween the time series of the middle spn in Fig. 12 nd of the top of the tower were clculted. We cn see tht the correltion coefficients re 0.701 nd 0.689, which demonstrtes the high correltion etween the middle spn nd the tower. Figure 13 shows the dynmic virtion response of the middle spn in the height (Z B ) component (Fig. 13) nd the time series of dominnt frequencies (Fig. 13-d).
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 13 of 15 c d Fig. 17 The dominnt frequency signls extrcted from displcement of top of the towers. The cutoff elevtion is 15 in GPS dt processing From Fig. 13, we know tht the first frequency is 0.104 Hz with corresponding mximum mplitude 18 mm under trffic lods. The mximum mplitudes for the other two frequencies 0.205 Hz nd 0.268 Hz re out 4 mm. Still, the first nturl frequency 0.104 Hz is plying the dominnt role in the mient excittion. Figure 14 illustrtes the longitudinl (X B ) deflections. The chngele rnge is from 2 cm to 4 cm in the longperiod component. The dynmic response is within 5 mm, nd the dominnt frequency is 0.15 Hz. From the correltion coefficients etween the displcement nd wind dt, the movement of the middle spn is lmost not dependent on the wind. Due to the stiffness of the ridge, nd significntly coupled with tht in the height (Z B ) direction, the movement chrcteristic in the longitudinl (X B ) component is complicted nd like pendulum, which needs more nlysis in the future. As for the tower, the low frequency term in the longitudinl (X B ) hs een nlysed previously. Due to the stiffness of the tower, for the lterl nd height components in Fig. 6, there is no ovious excittion response in the time series. The trend term is minly ecuse of multipth effect, which cn e eliminted y the siderel filter. The dynmic virtion signls for the three components re shown in Fig. 15. It cn e seen tht some dynmic responses in the longitudinl (X B ) component cn still e noticed. For the lterl (Y B ) nd height (Z B ) component, efore 16:30, the time series lmost demonstrtes the white noise chrcteristics. However, round 16:32, the mplitudes increse significntly. From Fig. 16d, the mplitude is incresing t the sme moment. There re two fctors cn cuse this: the excittions from wind, trffic or other lods nd the mesurement noise. After checking the wind dt in this period, the wind speed nd direction did not chnge nd the ig excittion from trffic lods is not t this period. Then, we improved the cut-off elevtion from 10 to 15 in the GNSS dt processing. The sme dominnt
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 14 of 15 frequencies time series in ll three directions re shown in Fig. 17. At the eginning epochs, one or two minutes re needed to fix the miguities with the cut-off elevtion of 15. The lrge mplitude is cused y the flot miguity resolutions. Except for the eginning time series, we cn find tht the high mplitude signl etween 16:30 nd 16:40 is missing in Fig. 17c, d. Then, we checked the stellite numer vrition during this period. At out 16:31:50, the elevtion of G17 ws exceeding 10 nd egn to e used in positioning. As is commonly known, the low elevtion signl cn esily e contminted y multipth effect nd residul tmospheric dely to contin high-level noise (Amiri-Simkooei nd Tierius, 2007). Therefore, the high-level noise cn propgte into the mplitude of virtion frequencies. Compred Fig. 16, with Fig. 17,, the excittion moment nd mplitude re lmost invrint. Tht mens only the nturl frequency of the tower ws effected y the noise in GNSS mesurements. Therefore, more nlysis should e done to figure out the effect of noise for dynmic response signl in SHM. However, these issues re eyond the scope of this study. Conclusions Structure helth monitoring nd ssessment for lrge ridges nd infrstructures re very importnt for the lifesfety nd current or future performnce of these systems. The GeoSHM system, conducted y the University of Nottinghm, intends to develop nd demonstrte novel system to tckle the issues in structurl deformtion monitoring of long ridges nd mke it possile for the ridge msters to fully understnd the loding nd response effect of the ridge, nd identify unusul deformtions under extreme wether conditions. Bsed on the reference monitoring system on the Forth Rod Bridge, the pper used the GNSS mesurements nd corresponding loding dt to nlyse the dynmic chrcteristic of the ridge. To support dt nlysis, moving verge filter ws employed to extrct the low frequency of the mient loding response. The results demonstrte tht, the movement of Forth Rod Bridge in the lterl (Y B ) component is minly dependent on the wind, nd it hs high correltion with the wind lodings t round 0.7. In the height (Z B ) component, the displcement of middle spn under the trffic lodings cn rech up to 0.3 m nd ecuse of the min cle linking the middle spn nd top of the tower, the movement time series of the top of the tower in the longitudinl (X B ) direction hs high correltion coefficient with the displcement of the middle spn. The displcement cn chieve up to 6 cm. In the lterl (Y B )ndheight(z B )component,dueto the stiffness of the tower, the trend term minly contins multipth effect nd possily the qusi-sttic displcement. Then, y FFT lgorithm nd ndpss filter, the dynmic virtion frequencies nd corresponding motion mplitude were extrcted from the Forth Rod Bridge under mient excittion lodings. It is found tht the first nturl frequencies of the middle spn of Forth Rod Bridge re 0.065 Hz, 0.15 Hz nd 0.104 Hz for lterl (Y B ), longitudinl (X B ) nd height (Z B ) components respectively. For the south tower, 0.18 Hz cn e shown in ll three directions, nd 0.104 Hz re shown in the longitudinl (X B ) component ecuse of the cles etween the tower nd middle spn. The nturl frequency of the longitudinl (X B ) direction of the ridge 0.15 Hz cn lso e shown in the time series. From the nlysis of this pper, we know tht the low frequency response of ridges nd dynmic virtion chrcteristics under mient lodings cn e reflected nd extrcted y GNSS technology. The monitoring informtion provided y GNSS is highly meningful for ridge msters in tht they cn use these dt sources for the decision mking of opening or closure nd mintennce or repir of the ridge. However, there re still some criticl prolems to e ddressed. For instnce, the noisy GNSS mesurements increse the mplitudes of virtion frequencies nd the second nd higher nturl frequencies with smll dynmic displcements cnnot e detected. In these cses, multi-constelltion GNSS systems nd integrtion with other sensors to collect loding nd responding dt with high reliility, will e the key for the success of the GeoSHM system. The GeoSHM tem includes vriety of experts for geomtics, civil engineering, computer science, communictions, etc. With the increse in new lrge ridges eing uilt in developing countries, especilly in Chin, nd some ridges in the developed countries hving een in service for more thn 50 yers, the GeoSHM system ecomes more nd more importnt in mking sure tht lrge ridges nd infrstructures re operting sfely. Acknowledgments The uthors would like to express their grtitude to the Europen Spce Agency for continuously sponsoring the GeoSHM Projects. In ddition, Amey PLC., Trnsport Scotlnd, Chin Rilwy Mjor Bridge Reconnissnce nd Design Institute Co., Ltd. nd Pnd GNSS Co., Ltd. re cknowledged for their resource inputs. Thnk two nonymous reviewers for their very constructive comments. Funding This work is supported y the Open Foundtion of Key Lortory of Precise Engineering nd Industry Surveying of Ntionl Administrtion of Surveying, Mpping nd Geoinformtion (Grnt No. PF2017 8). The Chinese Scholrship Council (CSC) hs provided the second uthor scholrship which llows him to visit the University of Nottinghm for 2 yers to reserch nd study in the UK from Novemer 2016. Authors contriutions XM proposed the initil ide, uilt the GeoSHM system nd revised this mnuscript; RX wrote this pper nd nlyzed the results of the experiments;
Meng et l. The Journl of Glol Positioning Systems (2018) 16:4 Pge 15 of 15 YX crried out the project implementtion. All uthors red nd pproved the finl mnuscript. Competing interests The uthors declre tht they hve no competing interests. Pulisher s Note Springer Nture remins neutrl with regrd to jurisdictionl clims in pulished mps nd institutionl ffilitions. Author detils 1 Nottinghm Geosptil Institute, The University of Nottinghm, Nottinghm NG7 2TU, UK. 2 School of Geodesy nd Geomtics, Wuhn University, 129 Luoyu Rod, Wuhn, Huei 430079, Chin. Received: 21 Septemer 2017 Accepted: 7 Mrch 2018 References Amiri-Simkooei AR, Tierius C (2007) Assessing receiver noise using GPS short seline time series. GPS Solutions 11(1):21 35 Breuer P, Chmielewski T, Górski P et l (2015) Monitoring horizontl displcements in verticl profile of tll industril chimney using glol positioning system technology for detecting dynmic chrcteristics. 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